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Relation between area and radius

Expert replies
by harsh.champ » Wed Feb 17, 2010 5:16 am
If the radius of a circle is increased by 20% then the area is increased by :

A. 44%
B. 120%
C. 144%
D. 40%
E. None of the above


The OA is A.

I used the following formula:-A = (pi)(r^2)
[spoiler]Hence,dA/dr = 2(pi)(r)

It seems shorter by using the derivative formula.[/spoiler]
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Source: — Problem Solving |

by ajith » Wed Feb 17, 2010 5:41 am
harsh.champ wrote:If the radius of a circle is increased by 20% then the area is increased by :

A. 44%
B. 120%
C. 144%
D. 40%
E. None of the above


The OA is A.

I used the following formula:-A = (pi)(r^2)
[spoiler]Hence,dA/dr = 2(pi)(r)

It seems shorter by using the derivative formula.[/spoiler]
If you the derivative circus, you will get an answer of 40%? if so, it is wrong

let r be the old radius and R be the new radius R = 1.2 r

old area = pi*r*r
new area = pi*1.2*1.2*r*r = 1.44 old area

the area increases by 44% not by 40%
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